Jody will be forced to repay a total of $2,377.69 when the loan matures.
Ordinary interest, commonly referred to as simple interest, is computed by dividing the annual marginal rate by the 365 days that make up a year. It does not take compounding into account.
The number of days can be calculated as follows:
19(Sep), 31(Oct), 30(Nov), and 31(Dec) add up to 111 days in year 1.
Second-year days: 26 (Jan)
137 days in total
Rate = 0.09 Principal = $2,300
time = 137 ÷ 365
Interest = 2300 × 0.09 × (137 ÷ 365) = $77.69
Amount due at maturity is $2,300 plus $77.69, for a total of $2,377.69.
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9. You Be the Teacher Is your cousin
correct? Explain.
4
MTR
14
X 0.82
28
+ 1120
1148
Find the absolute extrema for the given function on the interval [15.6, 19.2). Write your answer in the form (x.f(x)). Round your answers to two decimal places. f(x) = In (12x^2 - 11x + 2)
Absolute Minimum: Absolute Maximum
the absolute extrema of the linear equation f(x) = 12x^2 -11x +2 are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).
What are the absolute extrema of a linear equation within a closed interval?
According to the functions theory, linear equations have no absolute extrema for all real numbers, but things are different for any closed interval as absolute extrema are the ends of linear function. Now we proceed to evaluate the function at each point:
Absolute maximum
f(- 8) = 12x^2 -11x +2
f(- 8) = 27
Absolute minimum
f(4) = - 3 · 4 + 3
f(4) = - 9
By means of functions theory and the characteristics of linear equations, the absolute extrema of the linear equation f(x) = 12x^2 -11x+2 are 27 (absolute maximum) for x = - 8 and - 9 (absolute minimum) for x = 4. (- 8, 27) and (4, - 9).
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9. a baseball team has a total of 18 pitchers. the ratio of right-hand pitcher to total number of pitchers is 5:6. how many left-hand pitchers does the team have?
The number of Left Hand pitchers that the team have is 3 .
In the question ,
it is given that ,
the total number of pitchers in the baseball team is = 18
and the ratio of right hand to total pitchers is = 5 : 6
we have to find the number of left hand pitchers that the base ball team have .
From the ratio, the total number of pitchers is = 6x ,
and number of right hand pitchers = 5x ,
So , the number of left hand pitchers = x ,
that means , 6x = 18
Simplifying further ,
we get ,
x = 3,
Therefore , there are 3 left hand pitchers .
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2
52
3
5
4
47°
W
m/1 =
m/2 =
m/3=
m/4=
m25 =
Answer:55.9074
Step-by-step explanation:
two half-cylinders of diameter 2 meet at a right angle in the accompanying figure. find the volume of the solid region common to both half-cylinders. (hint: consider slices parallel to the base of the solid.)
The volume of the solid region common to both cylinder is 8/3 when two half-cylinders of diameter 2 come together at a right angle.
Given that,
In the following figure, two half-cylinders of diameter 2 come together at a right angle.
We have to determine the solid region's common volume for the two half-cylinders. (Hint: Take into account slices that are parallel to the solid's base.)
We know that,
Using the Pythagoras theorem,
S²+x²=r²
Diameter=2
2r=2
r=1
S²+x²=1
S²=1-x²
S=√(1-x²)
[tex]\int\limits^1_0 {Area(x)} \, dx[/tex]
4[tex]\int\limits^1_0 {1-x^{2} } \, dx[/tex]
4(x-x³/3)₀¹
4(1-1/3)
4(2/3)
8/3
Therefore, The volume of the solid region common to both cylinder is 8/3 when two half-cylinders of diameter 2 come together at a right angle.
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Camden found a bike on sale for $121. The sale was 45% off. How much money did Camden save on the bike because of the sale?
One measure of an angle in a triangle is 96°. The other two angle measures are represented by 2x and x + 12. Determine the other two degree measures for the missing angles
Answer:
Step-by-step explanation:
Measure of one angle= 96
one angle= 2x
other angle= x + 12
By using angle sum property, we know that sum of all angles in a triangle is 180 degree.
so,
96 + 2x + x+12 = 180
108 + 3x = 180
3x = 180 - 108
3x = 72
x = 72/3
x = 24
So,
one angle (2x) = 2 * 24
= 48
other angle ( x + 12 ) = 24 + 12
= 36
Hence, the other two degree measures for the missing angles is [tex]36[/tex].
What is the angles?
Angles are an integral facet in the study of mathematics, particularly geometry. Angles are formed by two rays (or lines) that begin at the same point or share the same endpoint.
The point at which the two rays meet (intersect) is called the vertex.
Here given that,
One measure of an angle in a triangle is [tex]96[/tex] degree. The other two angle measures are represented by [tex]2x[/tex] and [tex]x + 12[/tex].
So,
Measurement of one angle= [tex]96[/tex] degree
One angle= [tex]2x[/tex]
Other angle= [tex]x + 12[/tex]
As we know that sum of all angles in a triangle is [tex]180[/tex] degree.
So,
[tex]96 + 2x + x+12 = 180\\\\108 + 3x = 180\\\\3x = 180 - 108\\\\3x = 72\\\\x = \frac{72}{3}\\\\x = 24\\\\[/tex]
So,
One angle is
[tex](2x) = 2 (24)\\=48[/tex]
Other angle is ( x + 12 ) = 24 + 12
[tex]( x + 12 ) = 24 + 12\\=36[/tex]
Hence, the other two degree measures for the missing angles is [tex]36[/tex].
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scout troop 456 has 24 members. the scoutmaster appoints a 5-member campout crew composed of a leader, a cook, and a cleanup crew (3 scouts). how many different campout crews are possible?
As per the combination method, there are 42504 different campout crews are possible.
Combination method:
In math, combination method means a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.
Given,
Scout troop 456 has 24 members. the scoutmaster appoints a 5-member campout crew composed of a leader, a cook, and a cleanup crew (3 scouts).
Here we need to find the number of different campout crews are possible.
According to the nCr formula, here the value of
n = 24
And the value of r = 5
Then the number of possible combinations are calculated as,
=> ²⁴C₅ = 24!/5!(24 - 5)!
=> ²⁴C₅ = 24!/5!19!
=> ²⁴C₅ = 42504
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the minute hand of a clock is 6 inches long. how far does the tip of the minute hand move in 15 mintue?
The length of the minute hand is stated as r=6 inches. We are aware that the minute hand will create a 90° angle in 15 minutes. The measurement is 9.4248 inches as a result.
What is an angle?
An angle is a shape made up of two rays that share an endpoint and is known as the vertex of the angle. These rays are known as the sides of the angle. The plane that contains the rays contains the angles created by two rays. The meeting of two planes can also result in an angle. They are referred to as dihedral angles.
The orientation of a line with another line or plane is represented by its angular position. How far the body has been rotated from the reference position is used to measure angular position.
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what are the degrees of freedom used to test the significance of the slope in a simple linear regression equation? multiple choice n − 1 n − 2 n − 1, n − 2 (n − 1)(n − 2)
The degrees of freedom used to test the significance of the slope in a simple linear regression equation is n-2.
The maximum number of logically independent, or potentially different, values in the sample of data is referred to as the degree of freedom.
The degree of freedom is a fundamental concept that can be found throughout statistics in a variety of contexts, such as with hypothesis tests, probability distributions, and linear regression.
The degrees of freedom are n−k, however, in simple linear regression you estimate both a y-intercept and a slope, so k=2. Even though we generally don't worry about testing the intercept, it still uses up a degree of freedom, the slope would be very different and have a very different interpretation if we did not estimate an intercept along with the slope.
When we put the value of k=2 we get degrees of freedom are n-2.
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a parabola has one x-intercept at (– 4, 0). if the vertex is at (2, 5), find the other x-intercept.
The equation of the parabola is y -5 = (5/6) (x - 2)^2
How do you define a parabola?a curve produced by the intersection of a cone's surface with a plane perpendicular to a straight line; a curve produced by a moving point whose distance from a fixed point is equal to its distance from a fixed line.
What is the parabola on a graph?A quadratic function's U-shaped curve is shown on a parabola graph. A right circular cone and a plane surface intersect to form one of the conic sections known as a parabola in mathematics. The plane is symmetrical. U-shaped bend
y - k = a (x - h)2
where the vertex is (h,k). Since the vertex is known to be at (7,-3), we know that h = 7 and k = -3. Consequently, the equation is
y -5 = a (x - 2)2
We utilize the fact that the parabola passes through point to determine a for (4,0). With x =- 4 and y = 0, we obtain
0 - 5 = a (-4 - 2)
-5 = a (-6)2
-5 = -6a
a = 5/6
Consequently, the parabola's equation is
y -5 = (5/6) (x - 2)^2
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let ϕ : g → h be a homomorphism. (a) show that if h is abelian and ϕ is one-to-one, then g is abelian. (b) show that if g is abelian and ϕ is onto, then h is abelian. (c) if ϕ is an isomorphism, show that g is abelian if and only if h is.
When Ф(b)Ф(a) = Ф(ba) , then Ф is an isomorphism G is abelian
Let ϕ:G→H be an isomorphism.
If G is abelian, we have xy = yx , for any x,y ∈ G. Consider any two element in H , say c and d . Since Ф is an isomorphism , we have c = Ф(a) and d = Ф(b) for some a,b ∈ G . Hence,
cd = Ф(a)Ф(b) = (ab) =Ф(ba)
=Ф(b)Ф(a) = dc
This means H is an isomorphism.
If H is abelian, we have xy = yx, for any x,y ∈ H. Now consider two elements in G , say a and b .Since Ф is mapping , we have c = Ф (a) and d = Ф(b) for some c,d ∈ H. Hence ,
Ф(ab) = Ф(a)Ф(b) = cd = dc
= Ф(b)Ф(a) = Ф(ba)
Since, is an isomorphism , we have ab = ba ,
This means G is also abelian
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a) How many prime numbers are multiples of 5?
b) How many prime numbers are multiples of 8?
Answer:
afternoon and
a) =1
Step-by-step explanation:
because there is only one prime number in multiples of 5 that is 5
d) 1if the radius of a circle is 8 inches. What is the circle's area?
The circle's area is 200.96 square inches.
What is the area?
A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface. In general, square units such as square inches, square feet, etc. are used as the standard unit of area.
Any round form without edges or line segments is called a circle. In geometry, it has the shape of a closed curve.
radius, r = 8 inches
Area of a circle:
A = π r²
= 3.14 * 8²
= 200.96 square inches
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Cuál es la suma de 10 y -3
Answer: -6
Step-by-step explanation:
You're welcome I'm not sure if it corrects correct, but this is my answer
a new surgical procedure is said to be successful 90% of the time. suppose the procedure is performed five times. assume that the results of each procedure are independent of one another. in this binomial distribution application, which excel statement will find the probability of between 2 and 4, inclusively, successful surgical procedures?
The required probability is p(xS 2) =F(2).
Given that,
90% of the time, a novel surgical technique is deemed to be successful. Imagine that the technique is carried out five times. Count on the outcomes of each procedure being distinct from one another. in this application of the binomial distribution
BINOMDIST (2,5,90%, TRUE) is used to find the probability of 2 or fewer
to get 0.00856 because x =2 and n= 5 and TRUE indicates the cumulative
and the required probability is p(xS 2) =F(2)
Therefore, the required probability is p(xS 2) =F(2).
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Rewrite 4/6 : 1/3 as a unit rate
A. 2:1
B. 2:9
C. 12:9
D. 12:6
Answer: 2/1 should be your answer
Step-by-step explanation:
4 x 3= 12/6
1 x 3= 3/3
12 divided by 2 = 2 3 divided 3= 1
2/1
is the area of a circle directly proportional to the square of the radius. a circle with a radius of 10 has an area of 314. what will the are be on a circle of radius 4
The area of a circle with radius 4 is 50.24.
Writing the equation form for area and radius of two circles -
(Area/radius²) for circle 1 = (Area/radius²) for circle 2
Keep the values in the relation to find the area of small circle.
314/10² = Area/4²
Area = (314 × 16)/100
Performing multiplication on Right Hand Side of the equation to find the area of circle
Area = 5024/100
Performing division on Right Hand Side of the equation to find the area of circle
Area = 50.24
Hence, we see the decrease in area based on decrease in radius. Thus, the area of circle is 50.24.
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a rectangular tank that is 5234 ft^3 with a square base and open top is to be constructed of sheet steel of a given thickness. find the dimensions of the tank with minimum weight.
As per the volume of the rectangular tank, the dimensions are 13.78 x 379.82 x 13.78
Volume of rectangle:
The general formula to calculate the volume of the rectangle is
V = length x width x height.
Given,
A rectangular tank that is 5234 ft^3 with a square base and open top is to be constructed of sheet steel of a given thickness.
Here we need to find the dimensions of the rectangular tank,
As per the given volume of rectangular tank, when we equate this with the formula, then we get,
=> 5234 = length x width x height.
Let us consider the length and the width are equal then we get the value of height as.
=> height = 5234/length
So, the value is calculated by using the surface area formula,
=> A = length² + 5234/length
When we differentiate the surface area with respect to
=> dA/dl = 2l - 5234/l²
To minimize the surface area, so dA/dl = 0,
=> 2l = 5324/l²
=> 2l³ = 5234
=> l³ = 2617
=> l = ∛2617
Therefore, the value of length is 13.78
Then the height is calculated as.
=> h = 5234/13.78 = 379.82
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write a formula for f, the specific antiderivative of f. (remember to use absolute values where appropriate.) f(u)
The formula for f , the specific antiderivative of f is F(u) = 4㏑(u) + u²/2 + 11/2 .
In the question ,
it is given that ,
the function f(u) is f(u) = 4/u + u and f(1) = 6 ,
to find the antiderivative of f , we integrate it with respect to u ,
∫f(u) = 4∫(1/u)du + ∫u.du
On integrating ,
we get ,
F(u) = 4㏑(u) + u²/2 + c ......equation(1)
Substituting the value of u = 1 in equation(1) ,
we get ,
F(1) = 4㏑(1) + 1/2 + c
6 = 0 + 1/2 + c
c = 6 - 1/2
c = 11/2 .
Now , substituting the value of c = 11/2 in equation(1) , we get
F(u) = 4㏑(u) + u²/2 + 11/2
Therefore , the formula for f is F(u) = 4㏑(u) + u²/2 + 11/2 .
The given question is incomplete , the complete question is
Write a formula for f, the specific antiderivative of f.
f(u) = 4/u + u ; F(1) = 6 .
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the length of a model ship is 8 in its actual length is 100 ft what is the scale of the model
The scale of the model when the length of a model ship is 8 in its actual length is 100 ft is 1:150.
What is a scale?The term scale is used in mathematics to represent the relationship between a measurement on a model and the corresponding measurement on the actual object. Maps and blueprints would be useless without scales. A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size.
From the information, the length of a model ship is 8 in its actual length is 100 ft
It should be noted that;
1 foot = 12 inches
Therefore, 100 feet will be:
= 100 × 12
= 1200 inches
Therefore, the scale will be:
= 8/1200
= 1/150
= 1:150
The scale is 1:150.
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A 2. 8 kg rectangular air mattress is 2. 00 m long, 0. 500 m wide, and 0. 100 m thick. What mass can it support in water before sinking?.
The mass that can rectangular air mattress can support in water before sinking is 97.2 kg
Consider the rectangular air mattress
The length = 2 meter
The width = 0.500 meter
The thickness = 0.100 meters
The volume = Length × width × thickness
The volume = 2 × 0.500 × 0.100
= 0.1 cubic meters
We know,
Total weight = Volume × Density × g
The density of water = 1000 kg/ meter square
Total mass = 0.1 × 1000 × 9.81
= 981 N
The the equation of mass will be
(2.8 + m) × 9.81 = 981
2.8 + m = 100
m = 100 - 2.8
m = 97.2 kg
Therefore, it will support 97.2 kg water before sinking
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2. Theodore is writing the program for a video game. For one part of the game, he uses the rule (x, y) à (x + 4, y – 2) to move points on the screen. (a) What output does the rule give when the input is (7, -7)? Show your work. (b) What output does the rule give when the input is (-2, 0)? Show your work. (c) Is the rule a function? Explain why it is or why it is not.
Answer:
Step-by-step explanation:
find the probability of choosing a letter other than the letter a from a bag that contains the fifteen letters of the indian city palasa kasibugga. express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability of choosing a letter other than the letter a from a bag that contains the fifteen letters of the Indian city Palasa Kasibugga is 11/15.
According to the question,
We have the following information:
Words are:
Palasa Kasibugga
Now, total number of letters = 15
Number of a in these words = 4
Number of letters other than a = 11
We know that the following formula is used to find the probability of an event:
Probability = Number of favorable outcomes/total number of outcomes
Probability = 11/15
Hence, the probability of choosing a letter other than the letter a from a bag that contains the fifteen letters of the Indian city Palasa Kasibugga is 11/15.
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If Amy is tardy, then she will get a detention
Consider the INVERSE of this statement. What is the TRUTH VALUE of the INVERSE?
PLEASE THIS IS DUE IN 2 MINUTES
Answer:
Step-by-step explanation:
o
every rational number has a decimal expansion, so we could apply this same argument to show that the set of rational numbers between 0 and 1 is uncountable. however, because we know that any subset of q must be countable, the proof of theorem 1.6.1 must be flawed.
Every rational number can be expressed in decimal form. This argument cannot be used to demonstrate that rational numbers between 0 and 1 are countable. We frequently use this fact to demonstrate that rationals are countable since every rational number has a decimal representation that terminates on a non-teminating repeating sequence.
Rational number:
P/Q is the format for rational numbers, where p and q are open-ended integers and q 0. Thus, natural numbers, whole numbers, integers, fractions of integers, and decimals are all examples of rational numbers (terminating decimals and recurring decimals). The word "ratio" is where the word "rational" first appeared. Rational numbers are therefore closely tied to the idea of fractions, which stand for ratios. In other terms, a number is a rational number if it can be written as a fraction in which the numerator and denominator are both integers.
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i dont know what im doing please help
Answer:
x = 62°
Step-by-step explanation:
You want the base angle in an isosceles triangle with a vertex angle of 56°.
Isosceles triangle
The sides of any triangle are proportional to the sine of the opposite angle. When two sides have the same measure, their opposite angles will have the same measure. Since the sum of angles in a triangle is always 180*, this means ...
56° +x° +x° = 180°
2x = 124° . . . . . . . . . . subtract 56°
x = 62° . . . . . . . . . . divide by 2
The measure of the angle marked x is 62°.
__
Additional comment
The sides are all specified. This means you can find the angles of the triangle by solving it based on the side lengths. If you do that, you find that x ≈ 61.641°, as shown in the first attachment. This rounds to 62°.
As you can see in the second attachment, a better length for the side opposite the 56° angle would be 5.6 units instead of 5.7.
In short, the answer you get depends on how you use the given information.
<95141404393>
The effectiveness of a blood-pressure drug is being investigated.
An experimenter finds that, on average, the reduction in systolic blood pressure is 55.8 for a sample of size 29 and a standard deviation 7.9.
Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 90% confidence level).
Assume the data is from a normally distributed population.
Answer as a tri-linear inequality accurate to 3 decimal places.
A tri-linear inequality for the estimate of the drug that would lower a typical patient's systolic blood pressure (using a 90% confidence level) is; 53.3 ≤ x-bar ≤ 58.3.
Explain the term tri-linear inequality?Equal does not imply inequality. Tri signifies three. The range is defined in terms of inequalities by the tri-linear inequality.For the stated question-
Average of reduction in systolic blood pressure μ = 55.8.
Standard deviation s = 7.9.
Sample of size n = 29
The confidence interval is estimated as-
μ - t₀.₀₅(s/√n) ≤ x-bar ≤ μ + t₀.₀₅(s/√n)
Put the values-
55.8 - t₀.₀₅(7.9/√29) ≤ x-bar ≤ 55.8 + t₀.₀₅(7.9/√29)
On simplifying,
53.3 ≤ x-bar ≤ 58.3
Thus, a tri-linear inequality for the estimate of the drug that would lower a typical patient's systolic blood pressure (using a 90% confidence level) is; 53.3 ≤ x-bar ≤ 58.3.
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a scale drawing of an office space uses a scale of 1 in. : 6 yd. the scale drawing has an area of 6 square inches. what is the area of the actual office space?
The area of the actual office space is 36 yards if the scale is 1:6 yards.
An item is enlarged in a scale drawing. An expansion increases or decreases the size of an item by multiplying each of its lengths by a scale factor. A scale of 1:5, for instance, indicates that the size of 1 unit in the picture corresponds to the size of 5 units in the actual world.
The scale of office space is 1:6 yards. The scale drawing has an area of 6 square inches. This means that 1 scale represents 6 square inches of office. For the actual area multiply 6 by the area of the scale drawing which will give 36 yards.
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work out angle h
(simple circle theorems)
could someone help me with this? i will rate brainliest xx
Answer:
h = 90°
Step-by-step explanation:
You want the measure of the inscribed angle in a semicircle.
Inscribed angleAn inscribed angle has a measure equal to half the arc it subtends. Angle h intercepts the circle at the endpoints of a diameter, so subtends an arc of 180° (half a circle).
The measure of angle h is half of 180°, or 90°.
h = 90°
__
Additional comment
The fact that a triangle inscribed in a semicircle is a right triangle is useful for a variety of purposes. It is also useful to note that the circle center is the circumcenter, and is the midpoint of the hypotenuse.